TY - JOUR
T1 - Higher powers of quantum white noises in terms of integral kernel operators
AU - Chung, Dong Myung
AU - Ji, Un Cig
AU - Obata, Nobuaki
PY - 1998/10
Y1 - 1998/10
N2 - A rigorous mathematical formulation of higher powers of quantum white noises is given on the basis of the most recent theory of white noise distributions due to Cochran, Kuo and Sengupta. The renormalized quantum Itô formula due to Accardi, Lu and Volovich is derived from the renormalized product formula based on integral kernel operators on white noise functions. During the discussion, the analytic characterization of operator symbols and the expansion theorem for a white noise operator in terms of integral kernel operators are established.
AB - A rigorous mathematical formulation of higher powers of quantum white noises is given on the basis of the most recent theory of white noise distributions due to Cochran, Kuo and Sengupta. The renormalized quantum Itô formula due to Accardi, Lu and Volovich is derived from the renormalized product formula based on integral kernel operators on white noise functions. During the discussion, the analytic characterization of operator symbols and the expansion theorem for a white noise operator in terms of integral kernel operators are established.
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U2 - 10.1142/S0219025798000296
DO - 10.1142/S0219025798000296
M3 - Article
AN - SCOPUS:0000113513
SN - 0219-0257
VL - 1
SP - 533
EP - 559
JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics
JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics
IS - 4
ER -